Finite Group Databasebeta

← C13×#9387 #15695726

Subgroups — C13×#9387 #15695726

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2873C211yesmaximal, characteristic, complemented
2C13×#2610C211yesmaximal, characteristic
3C13×#1527C212yesmaximal, complemented
4C13×#1464C211yesmaximal, characteristic, complemented
5C13×#1300C212yesmaximal, complemented
6C22×C13×M16—21no—
7C2×C13×#124C2211yescharacteristic
8C2×C13×#117C2211yescharacteristic
9C13×#432C2212yes—
10C13×#405—24no—
11C4×C13×M16—21no—
12C4×C13×M16C2212yes—
13C13×#395C411yescharacteristic
14C13×#394C411yescharacteristic
15C13×#393C411yescharacteristic
16C13×#392C411yescharacteristic
17C13×#390—21no—
18C13×#388—21no—
19C13×#388—21no—
20C13×#386—21no—
21C13×#376C2211yescharacteristic
22C13×#329—24no—
23C13×#324—21no—
24C13×#323—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C2×C13×M16—22no—
30C2×C13×M16—24no—
31C2×C13×M16—24no—
32C2×C13×M16—22no—
33C22×C8×C13—22no—
34C13×#124—22no—
35C13×#124—22no—
36C13×#117—22no—
37C13×#117—22no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C42×C13—21no—
50C2×C42×C13D411yescharacteristic
51C2×C42×C13C2311yescharacteristic
52C13×C4⋊C8—22no—
53C13×C22⋊C8—22no—
54C13×#97—22no—
55C13×#97—22no—
56C13×#97D414yescomplemented
57C4×C8×C13—22no—
58C4×C8×C13—22no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95C2×C411yescharacteristic
63C13×#95C2×C411yescharacteristic
64#9387C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C24×C13C22⋊C411yescharacteristic
67C2×Q8×C13—22no—
68C2×Q8×C13—81no—
69C2×D4×C13—22no—
70C2×D4×C13—42no—
71C2×D4×C13—42no—
72C2×D4×C13—81no—
73C2×D4×C13—81no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C13×M16—28no—
88C13×M16—24no—
89C13×M16—24no—
90C2×C8×C13—28no—
91C2×C8×C13—24no—
92C2×C8×C13—42no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—81no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—81no—
104C13×C22⋊C4—81no—
105C42×C13—21no—
106C42×C13—21no—
107C42×C13—42no—
108C42×C13C2×D412yes—
109C42×C13#4112yes—
110#2873C2×C1311yescharacteristic, complemented
111#2610C2×C1311yescharacteristic
112#1527C2×C1312yescomplemented
113#1464C2×C1311yescharacteristic, complemented
114#1300C2×C1312yescomplemented
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13#10412yes—
127C23×C13C2×C22⋊C411yescharacteristic
128Q8×C13—82no—
129D4×C13—82no—
130D4×C13—84no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—24no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—22no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13#10412yes—
154C2×C4×C13C4×D412yes—
155C2×C4×C13#12011yescharacteristic
156C2×C4×C13#12112yes—
157C2×C4×C13#12311yescharacteristic
158C8×C13—28no—
159C8×C13—82no—
160C22×M16—21no—
161C2×#124C22×C1311yescharacteristic
162C2×#117C22×C1311yescharacteristic
163#432C22×C1312yes—
164#405—24no—
165C4×M16—21no—
166C4×M16C22×C1312yes—
167#395C4×C1311yescharacteristic
168#394C4×C1311yescharacteristic
169#393C4×C1311yescharacteristic
170#392C4×C1311yescharacteristic
171#390—21no—
172#388—21no—
173#388—21no—
174#386—21no—
175#376C22×C1311yescharacteristic
176#329—24no—
177#324—21no—
178#323—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—22no—
182C22×C13—42no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13—81no—
193C22×C13#38611yescharacteristic
194C22×C13C2×#10411yescharacteristic
195C22×C13C2×#10411yescharacteristic
196C4×C13—22no—
197C4×C13—21no—
198C4×C13—22no—
199C4×C13—21no—
200C4×C13—22no—
201C4×C13—42no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13—81no—
205C4×C13—81no—
206C22×Q8C2×C4×C1311yescharacteristic
207C22×D4—21no—
208C22×D4C2×C4×C1311yescharacteristic
209C23×C4D4×C1311yescharacteristic
210C2×M16—22no—
211C2×M16—24no—
212C2×M16—24no—
213C2×M16—22no—
214C22×C8—22no—
215#124—22no—
216#124—22no—
217#117—22no—
218#117—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×C4×C1311yescharacteristic
221C2×C4⋊C4D4×C1311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4C2×C4×C1311yescharacteristic
229C2×C22⋊C4D4×C1311yescharacteristic
230C2×C42—21no—
231C2×C42D4×C1311yescharacteristic
232C2×C42C23×C1311yescharacteristic
233C4⋊C8—22no—
234C22⋊C8—22no—
235#97—22no—
236#97—22no—
237#97D4×C1314yescomplemented
238C4×C8—22no—
239C4×C8—22no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95C2×C4×C1311yescharacteristic
244#95C2×C4×C1311yescharacteristic
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—42no—
248C2×C13—161no—
249C2×C13#188411yescharacteristic
250C2×C13#189611yescharacteristic
251C2×C13#191411yescharacteristic
252C24—21no—
253C24C13×C22⋊C411yescharacteristic
254C2×Q8—22no—
255C2×Q8—81no—
256C2×D4—22no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—81no—
260C2×D4—81no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4C13×C22⋊C411yescharacteristic
269C22×C4C13×C22⋊C411yescharacteristic
270C22×C4C13×C22⋊C411yescharacteristic
271C22×C4C22×C4×C1311yescharacteristic
272C22×C4C2×D4×C1311yescharacteristic
273C22×C4C2×D4×C1311yescharacteristic
274M16—28no—
275M16—24no—
276M16—24no—
277C2×C8—28no—
278C2×C8—24no—
279C2×C8—42no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—81no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—41no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C42—21no—
293C42—21no—
294C42—42no—
295C42C2×D4×C1312yes—
296C42C13×#4112yes—
297C13#938711yescharacteristic, direct product factor, Sylow
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23C13×#10412yes—
310C23C2×C13×C22⋊C411yescharacteristic
311Q8—82no—
312D4—82no—
313D4—84no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4C13×#10412yes—
337C2×C4C4×D4×C1312yes—
338C2×C4C13×#12011yescharacteristic
339C2×C4C13×#12112yes—
340C2×C4C13×#12311yescharacteristic
341C8—28no—
342C8—82no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C13×#38611yescharacteristic
358C22C2×C13×#10411yescharacteristic
359C22C2×C13×#10411yescharacteristic
360C4—22no—
361C4—21no—
362C4—22no—
363C4—21no—
364C4—22no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2C13×#188411yescharacteristic
375C2C13×#189611yescharacteristic
376C2C13×#191411yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#392C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C13×#2873C2semidirect
3. C13×#1527C2semidirect
4. C13×#1464C2semidirect
5. C13×#1300C2semidirect
56. C13×#97D4semidirect
64. #9387C13direct (N × H)
110. #2873C2×C13semidirect
112. #1527C2×C13semidirect
113. #1464C2×C13semidirect
114. #1300C2×C13semidirect
237. #97D4×C13semidirect
297. C13#9387direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×#28732
C13×#26102
C13×#15272
C13×#14642
C13×#13002
#938713